At first glance, it may be a simple matter of backing up the database (which holds all the network/sites tables) and injecting it in your production database (using phpmyadmin for instance). You will need to seek and replace in the sql file all references to your local server and replace with domain name (make a backup copy first).
Tables you will need to go through:
wp_posts, wp_ x _posts, wp_site, wp_blogs, wp_options, wp_ x _options (where you will modify the fields home, siteurl, fileupload_url).
You can safely search and replace in the wp_posts and variants tables (replace localhost refs with http://domain.tld/), whereas you will need to manually go through the wp_options and variants. Read the fields carefully, it should be self-explanatory once you get used to looking at them :)
If your database / database user / password changes from your local environment to prod, modify the wp-config.php file to reflect these changes. Make sure "localhost" works on your production server.
Then, you would need to upload your WP files to your public HTML directory on the prod server.
Finally, you would need to configure domain mapping (in your cPanel or other server admin panel, setting up wildcard / subdomains) so that your main site and subsites can be accessed by the browser.
Basically, it's pretty much the same as migrating a single install, with the added need to correctly map your subdomains on the server and replace server references in a couple more places in db.